A342957 a(n) is the least k such that A342956(k) = n.

1, 2, 4, 15, 39, 87, 183, 951, 1255, 1527, 3063, 15335, 12279, 61431, 49143, 516047, 491495, 1703767, 1310695, 8257487, 3145719, 15728631, 12582903, 94371815, 50331639, 352321527, 335544295

Offset

0,2

Comments

a(n) exists for all n, as A342956(2^(2^k)) = k+1.

If 2^n = p+q where p and q are primes, then A342956(p*q) = n so a(n) <= p*q <= 2^(2*n-2). Goldbach's conjecture implies such p and q exist for all n >= 2.

Links

Table of n, a(n) for n=0..26.

Example

a(3) = 15 because A342956(15) = 3 and this is the first appearance of the value 3 in A342956.

Maple

f:= proc(n) local t; numtheory:-bigomega(add(t[1]*t[2], t=ifactors(n)[2])) end proc:
V:= Array(0..18): count:= 0:
for n from 0 while count < 19 do
v:= f(n):
if v <= 19 and V[v] = 0 then
    count:= count+1; V[v]:= n
fi
od:
convert(V, list);

Mathematica

Table[n=0; While[PrimeOmega[Plus@@Times@@@FactorInteger@++n]!=k]; n, {k, 0, 14}] (* Giorgos Kalogeropoulos, Aug 20 2021 *)

Crossrefs

Cf. A342956.

Sequence in context: A153945 A153942 A055466 * A148267 A148268 A148269

Adjacent sequences: A342954 A342955 A342956 * A342958 A342959 A342960

Keyword

nonn,more

Author

J. M. Bergot and Robert Israel, Mar 30 2021

Extensions

a(25)-a(26) from Chai Wah Wu, Mar 31 2021

Status

approved